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Advancement: Nonparametric Bayesian Modeling for Spatial Point Processes

Speaker Name: 
Chunyi Zhao
Speaker Title: 
Ph.D. Student
Start Time: 
Friday, May 29, 2020 - 1:00pm
End Time: 
Friday, May 29, 2020 - 3:00pm
Location: 
Zoom - https://ucsc.zoom.us/j/98500467897

Abstract: Spatial point processes are stochastic models for spatial point patterns that record the locations of a certain event in a bounded observation window. Our research aims to explore flexible and computationally efficient Bayesian nonparametric prior models for non-homogeneous Poisson processes and for spatial Hawkes processes, a practically important extension that incorporates clustering structure. We first consider modeling Poisson process intensity functions through a weighted combination of structured beta densities, a model construction that implies a Bernstein Dirichlet process prior for the Poisson process density, thus supporting flexible inference for point process functionals. A key feature of this methodology is that it balances such model flexibility with computational efficiency in the implementation of posterior inference, which is particularly important in applications where spatial point patterns are recorded over irregu! lar domains. We then relax the independence assumption of the Poisson process and explore the class of cluster point processes that allows for correlation among points and for more general stochastic mechanisms for spatial point patterns, while maintaining a connection to the Poisson process. We focus on modeling the spatial Hawkes process with its connection to the general shot noise Cox process in a hierarchical formulation that fits naturally in our nonparametric Bayesian framework. Under such a framework, we aim to explore models with a nonparametric prior on either the immigrant process intensity or the offspring process density, that can be used for different applications. Finally, in the context of an immunotherapy application, we propose a Bayesian hierarchical model to handle inference based on replicates from the same point process over different observation domains, and to jointly model a collection of covariate-dependent point processes.

Event Type: 
Adancement/Defense
Advisor: 
Athanasios Kottas
Graduate Program: 
Statistical Science